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Old 19th September 2008, 10:08   #1
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Default How to deduce top speed of a car without breaking speed limit

[Mods, please move this post if it is not in the appropriate place]

I have seen quite a good number of posts about the top speeds of different vehicles. Some try to arrive using power, torque, weight of the vehicle blah blah. This is how the top speed of a car can be arrived at without really trying the limit.

The factors that influence the top speed of a car:
  1. Maximum rpm the engine can do (same in any gear)
  2. Gear ratio at each gear (whose top speed will be different)
  3. Diameter of the wheel tyre.
  4. Differential ratio of the transmission to wheel axle
Without even driving the car, we should be able to arrive at the top speed if we have these three parameters. However if we have a car, we can do without any of the above parameters. Of course we are going to find out the maximum rpm the engine can do (could be different from what the manufacturer claim depending on the age of the engine).

Test the top speed in first gear in a high way and note down the rpm the car is capable of reving. Let's call that R.

Now, note down the speed at 2000 rpm in a given gear, x. Let's call that Sx.

Now the top speed Tx in x gear will be:

Tx = R * Sx / 2000

(For those unfamiliar with computer language, * denotes multiplication)

As we can see, top speed has no relation with the power or torque or load/weight. The catch here is that the engine can pull the vehicle only if it has enough torque to cause an acceleration greater than zero. Even the tiniest of torque can cause an acceleration greater than zero provided there is no opposite force, such as going uphill or wind resistence. In most practical cases, assuming plane surface and negligible wind speed (when car is not moving), any car will have sufficient torque to pull most loads against the wind speed (increasing at higher speed of the vehicle).

As we can also see, the top speed will increase if the tyre diameter is increased.

Anyone who is expert on gear ratio can add on how to arrive at the top speed from known tyre specs and gear ratios.

I did further reading from Gear ratio - Wikipedia, the free encyclopedia
It indicates that there is another reduction from the transmission to the actual wheel, they term it as differential ratio. They have also explained how to arrive at the speed

Last edited by opendro : 19th September 2008 at 10:25. Reason: Added another parameter "differential ratio
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Old 19th September 2008, 11:32   #2
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What you're talking about is mechanical top speed (provided this is achieved before a vehicle hits its aerodynamical top speed).

There are many other factors that decide the actual top speed of a vehicle.

My car has a mechanical top speed of 250kmph meaning, i can touch 250kmph provided i can redline (7100rpm) 5th gear. But this is not possible coz the power, torque, weight and aerodynamical properties of my car limit it to 185kmph (5237rpm in 5th).

Quote:
As we can also see, the top speed will increase if the tyre diameter is increased.
If this was true, wouldn't the monster trucks/big foots be capable of 500-600kmph top whacks? What a bigger wheel does is reduce the wheel rpm at your vehciles top speed. If you put bigger diameter wheels on a Zen you will not see an increase in top speed. Infact if the bigger wheel is heavier than the stock wheel, you might actually see a drop in top speed.

So please don't confuse mechanical top speed with aerodynamical top speed.

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Old 19th September 2008, 11:38   #3
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Quote:
Originally Posted by opendro View Post
[*]Maximum rpm the engine can do (same in any gear)
I have only seen some diesels hit max rpm in 5th gear. AFAIK, no Indian petrol car does.

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Originally Posted by Shan2nu View Post
What a bigger wheel does is reduce the wheel rpm at your vehciles top speed. If you put bigger diameter wheels on a Zen you will not see an increase in top speed.
True. But it may increase the max speed of lower gears.
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Old 19th September 2008, 11:43   #4
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Forgive the cheek, but...

Take the car to an unregulated freeway like the fabled Highway to Hell and find out!
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Old 19th September 2008, 11:54   #5
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Quote:
True. But it may increase the max speed of lower gears.
Yes it will.

Prob the only way you can see a slight increase in actual top speed is if your bigger wheels are way lighter than your stock wheels. So its a combination of size and weight that decides if your top speed will increase or decrease.

Shan2nu

Last edited by Shan2nu : 19th September 2008 at 11:56.
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Old 19th September 2008, 12:03   #6
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Hi Opendro, like Shan2nu had mentioned just considering drive-line gearing & wheel dimensions would result in top-speeds you can't achieve in real life. You could do it on a chassis dyno though, I guess.

The thing that stops you is aerodynamic drag, which is why if you sky-dive you'll not top 196 Kmph (terminal velocity). Plus, you'll have to contend with rolling resistance. Aero Drag is function of your car's drag coefficient (Cd), frontal area, air density & finally the square of your speed.

Rolling resistance, on the other hand, is a function of coefficient of rolling resistance & the weight of your car.

Cd values are usually included in a car's specifications, frontal area is not...
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Old 19th September 2008, 13:35   #7
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I DID mention that the car should have enough torque to cause an acceleration greater than zero against all opposite forces (read as resistence). I believe most cars today will have enough torque to cause a positive acceleration (on plane surface, with no wind speed at vehicle idle). But the acceleration may be so small that you will take very LONG TIME to actually reach the top speed. Good torque ones will manage to reach the top speed much easily as it would cause enough acceleration against resistances.

As GTO mentioned, some petrol vehicles may not be able to red line at all in fifth gear as the resultant torque on the wheel will be less than the opposite resistance at higher speed. Or even if the torque is greater, it would have taken very long time if it is marginally greater than the resistances (all put together).

Shan2nu, how do you say that trucks will do 500-600? Engine torques are converted to wheels rotating torque by various gear reductions. Trucks are obviously designed to result in a huge torque on the final axle, not to do very high rpm on the wheels. I suggest you read Gear ratio - Wikipedia, the free encyclopedia about how the wheels speed is related to engine speed. And I also suggest that you read HowStuffWorks "How Gears Work" to understand how different torque results are produced on the wheel from the engines.
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Old 19th September 2008, 13:38   #8
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At high speeds the equation becomes a bit more complex since there will be a change in the downforce acting on the car. Also the top speed will be different at different periods of time due to factors such as altitude, humidity and temperature.
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Old 19th September 2008, 13:44   #9
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Quote:
Shan2nu, how do you say that trucks will do 500-600?
U took it too serious dude. That was just a joke.

Coz you said that top speed can be increased with bigger wheels which doesn't always work. I can't really increase the top speed of my car by using 25" wheels can i?

How can you possibly say that top speed has no relation with power, torque, weight etc

It just is.

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Old 19th September 2008, 14:05   #10
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Quote:
Originally Posted by Shan2nu View Post
How can you possibly say that top speed has no relation with power, torque, weight etc
Assume that a car will need an engine that can produce 200Nm of torque at it max rpm 6000 rpm and assume that the car needs 100Nm of engine torque to reach 6000 rpm in fift gear in real driving condition with five adults, lets say.

Assume that engine is tweaked to produce 800Nm of engine torque at 6000 rpm. It will obviously boost the power at 6000rpm to four times. Now, this increase in torque and power (four times for both) is not going to result higher top speed.

That was my point. And let me remind you again that I mentioned that there is a minimum torque that is required to counter the resistance at increasing speed before it reaches the top. GTO said that the car may not red line (reason being the minimum torque not being met, as I would understand) and I'm fine with that. You are talking as if top speed is directly related with torque, power, load, etc. etc. which I don't agree and I'm giving the reason also.

Last edited by opendro : 19th September 2008 at 14:06.
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Old 19th September 2008, 14:05   #11
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Quote:
Now, note down the speed at 2000 rpm in a given gear, x. Let's call that Sx.

Now the top speed Tx in x gear will be:

Tx = R * Sx / 2000
I didn't understand this formula.

Can you give us an example as to how it works.

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Old 19th September 2008, 14:10   #12
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Quote:
That was my point. And let me remind you again that I mentioned that there is a minimum torque that is required to counter the resistance at increasing speed before it reaches the top. GTO said that the car may not red line (reason being the minimum torque not being met, as I would understand) and I'm fine with that. You are talking as if top speed is directly related with torque, power, load, etc. etc. which I don't agree and I'm giving the reason also.
So if a Bugatti Veryon had 500bhp and 500nm of torque (everything else being equal), what do you feel it's top speed would be?

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Old 19th September 2008, 14:16   #13
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Quote:
Originally Posted by Shan2nu View Post
I didn't understand this formula.

Can you give us an example as to how it works.

Shan2nu
If you had read the wiki, you would have understood. Anyway, let me tell in simple exmple:

Suppose, when you pedal your cycle in a given gear at 40 rpm, assume the wheel will rotate at 100 rpm, let's say equivalent to 20 Kmph speed. Now you pedal at 80 rpm, the wheel will now rotate at 200 rpm causing the speed to double at 40Kmph.

To generalize, rpm of your pedal, the cycle's speed will be:

speed = rpm * 20 / 40

Assuming you can pedal at max 100 rpm even without any friction with the wheel rotating in the air, your top speed will be
100 * 20 / 40 = 50Kmph.

Again my assumption that you have much more strength than the resistance that will come at 50Kmph
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Old 19th September 2008, 14:17   #14
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I agree with Shan2nu. At low speeds the limiting factor would probably be the transmission and gear ratio. But at medium to high speeds (> 120 kmph) the air drag will be the most significant factor for determining the top speed. So torque would play a significant part here.

Last edited by watashi75 : 19th September 2008 at 14:23. Reason: Edited.
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Old 19th September 2008, 14:20   #15
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Quote:
Originally Posted by Shan2nu View Post
So if a Bugatti Veryon had 500bhp and 500nm of torque (everything else being equal), what do you feel it's top speed would be?

Shan2nu
Final drivingshaft (wheel) speed can be increased with a different gear ratio as I mentioned. If the Bugati had a fifth gear ratio of 6000:1 and differential ratio (from transmission to final drive shaft) of 1:1, the maximum speed it can do is to rotate its tyres only once per minute. What will be the use of that torque now?
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